Alzheimer’s disease (AD) is a severe neurodegenerative disorder of the brain that manifests as dementia, disorientation, difficulty in speech, and progressive cognitive and behavioral impairment. The emerging therapeutic approach to AD management is the inhibition of β-site APP cleaving enzyme-1 (BACE1), known to be one of the two aspartyl proteases that cleave β-amyloid precursor protein (APP). Studies confirmed the association of high BACE1 activity with the proficiency in the formation of β-amyloid-containing neurotic plaques, the characteristics of AD. Only a few FDA-approved BACE1 inhibitors are available in the market, but their adverse off-target effects limit their usage. In this paper, we have used both ligand-based and target-based approaches for drug design. The QSAR study entails creating a multivariate GA-MLR (Genetic Algorithm-Multilinear Regression) model using 552 molecules with acceptable statistical performance (R² = 0.82, Q²_loo = 0.81). According to the QSAR study, the activity has a strong link with various atoms such as aromatic carbons and ring Sulfur, acceptor atoms, sp2-hybridized oxygen, etc. Following that, a database of 26,467 food compounds was primarily used for QSAR-based virtual screening accompanied by the application of the Lipinski rule of five; the elimination of duplicates, salts, and metal derivatives resulted in a truncated dataset of 8,453 molecules. The molecular descriptor was calculated and a well-validated 6-parametric version of the QSAR model was used to predict the bioactivity of the 8,453 food compounds. Following this, the food compounds whose predicted activity (pKi) was observed above 7.0 M were further docked into the BACE1 receptor which gave rise to the Identification of 4-(3,4-Dihydroxyphenyl)-2-hydroxy-1H-phenalen-1-one (PubChem I.D: 4468; Food I.D: FDB017657) as a hit molecule (Binding Affinity = −8.9 kcal/mol, pKi = 7.97 nM, Ki = 10.715 M). Furthermore, molecular dynamics simulation for 150 ns and molecular mechanics generalized born and surface area (MMGBSA) study aided in identifying structural motifs involved in interactions with the BACE1 enzyme. Molecular docking and QSAR yielded complementary and congruent results. The validated analyses can be used to improve a drug/lead candidate’s inhibitory efficacy against the BACE1. Thus, our approach is expected to widen the field of study of repurposing nutraceuticals into neuroprotective as well as anti-cancer and anti-viral therapeutic interventions.